Sorry, I'm confused. What are the hoops? Wouldn't this be solved by Persona just telling the IdP the URL of the site to auth to?
3rd party cookie blocking makes this worse, since it’s difficult to silently refresh your session by checking with the IdP behind the scenes. I believe Auth0 uses a hidden iframe for this, which uses 3rd party cookies and looks a lot like a tracking pixel. Without that refresh mechanism, though, relying parties are pushed to have longer lived sessions, which makes the lack of a global revocation worse.